• SJSU Singular Matrix Database
• Matrix group: GHS_indef
• Click here for a description of the GHS_indef group.
• Click here for a list of all matrices
• Click here for a list of all matrix groups

• Matrix: GHS_indef/ncvxqp1
• Description: Gould, Hu, & Scott: KKT matrix - nonconvex QP (CUTEr)
• download as a MATLAB mat-file, file size: 323 KB. Use SJget(481) or SJget('GHS_indef/ncvxqp1') in MATLAB.
• download in Matrix Market format, file size: 256 KB.
• download in Rutherford/Boeing format, file size: 259 KB.

A singular value of A is guaranteed1 to be in the interval pictured by the blue bars around each of the calculated singular values.

Routine svds_err, version 1.0, used with Matlab 7.6.0.324 (R2008a) to calculate the 6 largest singular values and associated error bounds.
Routine spnrank, version 1.0 with opts.tol_eigs = 1e-008, used with Matlab 7.6.0.324 (R2008a) to calculate singular values 7085 to 7090 and associated error bounds.

 Matrix properties (click for a legend) number of rows 12,111 number of columns 12,111 structural full rank? yes structural rank 12,111 numerical rank 7,087 dimension of the numerical null space 5,024 numerical rank / min(size(A)) 0.58517 Euclidean norm of A 7.5802e+012 calculated singular value # 7087 12.93 numerical rank defined using a tolerance max(size(A))*eps(norm(A)) = 11.827 calculated singular value # 7088 7.4116 gap in the singular values at the numerical rank: singular value # 7087 / singular value # 7088 1.7446 calculated condition number -2 condest 2.424e+029 nonzeros 73,963 # of blocks from dmperm 1 # strongly connected comp. 1 entries not in dmperm blocks 0 explicit zero entries 0 nonzero pattern symmetry symmetric numeric value symmetry symmetric type real structure symmetric Cholesky candidate? no positive definite? no

 author N. Gould editor N. Gould date 1994 kind optimization problem 2D/3D problem? no SJid 481 UFid 1,242

 Ordering statistics: AMD METIS nnz(chol(P*(A+A'+s*I)*P')) 2,222,105 1,280,499 Cholesky flop count 2.2e+009 6.2e+008 nnz(L+U), no partial pivoting 4,432,099 2,548,887 nnz(V) for QR, upper bound nnz(L) for LU 6,506,571 2,972,102 nnz(R) for QR, upper bound nnz(U) for LU 14,173,093 6,554,101

Maintained by Leslie Foster, last updated 24-Apr-2009.

Entries 5 through 14 in the table of matrix properties and the singular
value plot were created using SJsingular code. The other plots
and statistics are produced using utilities from the SuiteSparse package.
Matrix color plot pictures by cspy, a MATLAB function in the CSparse package.